When my application written in Java with SWT runs under OS X, both from under Eclipse and from jar, its name in
You should create a macOS app bundle with your jar, where you can put the bundle display name in the Info.plist file of the bundle.This is well documented by Oracle (http://docs.oracle.com/javase/7/docs/technotes/guides/jweb/packagingAppsForMac.html).
The structure of a Java app bundle is documented by Apple as well: https://developer.apple.com/library/content/documentation/Java/Conceptual/Java14Development/03-JavaDeployment/JavaDeployment.html